Answer
$\overline {x} =\dfrac{33}{85}; , \overline {y} =\dfrac{698}{595}$
Work Step by Step
We have $\overline {x}=\dfrac{12}{17} \int_{0}^{1} x\cdot (2-x^3-x^2) dx $
or, $=(\dfrac{12}{17}) \times [x^2- \dfrac{x^5}{5}-\dfrac{x^4}{4}]_{0}^{1}$
or, $\overline{x}=\dfrac{33}{85}$
and $\space \overline {y}=\dfrac{12}{17} \int_{0}^{1} (2-x^3-x^2)
\times \dfrac{(2+x^3+x^2)}{2}dx$
or, $\overline {y} =\dfrac{6}{17} [4x- \dfrac{x^7}{7}+\dfrac{x^6}{3}-\dfrac{x^5}{5}]_{0}^{1}$
or, $\overline {y}=\dfrac{698}{595}$
